Two terms of a geometric sequence are a5=2500 and a8=312,500 Write an explicit rule for the nth term

Answer:

the first option is the correct answer

x^2-2/7x+7

Step-by-step explanation:

Answer:

26 min

Step-by-step explanation:

The slope of the data will be equal to 2 for the book reading.

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. The slope is also defined as the ratio of the rise to the run of the line.

Given that Jenny started reading her book for English class at 8:03 p.m. and she started on page 24. At 8:29 p.m., Jenny stopped reading and was on page 37.

The slope of the data will be calculated as,

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( 29 - 3) / ( 37 - 24)

Slope = 2

Therefore, the slope of the data will be equal to 2 for the book reading.

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The function that represents the Scooter Company's total profit is option A) -2x^2 + 200x - 1,500. This function represents the difference between the total revenue and the total cost, taking into account the cost per scooter and the fixed cost. Option A

To determine the function that represents the Scooter Company's total profit, we need to subtract the total cost from the total revenue.

The total cost is given by the formula:

Total Cost = Cost per scooter * Number of scooters + Fixed cost

In this case, the cost per scooter is $200 and the fixed cost is $1,500.

Total Cost = 200x + 1,500

The total revenue is given by the function:

Total Revenue = R(x) = 400x − 2x^2

To calculate the profit, we subtract the total cost from the total revenue:

Profit = Total Revenue - Total Cost

Profit = (400x - 2x^2) - (200x + 1,500)

Simplifying the expression, we get:

Profit = 400x - 2x^2 - 200x - 1,500

Rearranging the terms, we have:

Profit = -2x^2 + 200x - 1,500

Option A

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Answer:

first one is 24

second one is probably 12

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

On each median, the distance from the vertex to the centroid is twice as long as the centroid to the midpoint , that is

BO = 2 × OY = 2 × 12 = 24

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the altitude DB is at right angles to AC , then ∠ CBD = 90°

sum the 3 angles in Δ BCD and equate to 180

10x - 14 + 4x - 8 + 90 = 180

14x + 68 = 180 ( subtract 68 from both sides )

14x = 112 ( divide both sides by 14 )

x = 8

Answer:

Step-by-step explanation:

slope is -1/3

y=-1/3x+b

take the point (1,0) and put in the equation

0=-1/3(-1)+b

0=1/3+b

-1/3+0=-1/3+1/3+b

-1/3=b

y=-1/3-1/3

Answer:

1407.43 would be your answer

Step-by-step explanation:

The formula is \(\pi r^2h\), so plug 8 and 7 into the equation, and you'll get your answer. Hope this helps :)

Answer:

b. Contains four right angles.

Step-by-step explanation:

A parallelogram has two pairs of opposite sides that are both congruent and parallel, as does a rectangle.

A parallelogram usually does NOT have four right angles, but a rectangle does. b Contains four right angles is the difference between a parallelogram and a rectangle.

The diagonals of a parallelogram bisect each other, and so do the rectangle's diagonals.

The opposite angles of parallelograms are congruent, and all four angles of a rectangle are congruent, so this is a similar aspect of both a parallelogram and a rectangle.

Hope this helps!

An expression that is equivalent to ∛18⁴ is (b) (18)³/⁴

From the question, we have the following parameters that can be used in our computation:

∛18⁴

Applying the law of indices, we have

∛18⁴ = (18⁴)¹/³

Evaluate

So, we have

∛18⁴ = (18)³/⁴

Hence, the solution is (18)³/⁴

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Answer:

A) $75

B) y = 30x + 15

C) (24, 735) **graph below

D) Yes, there is a proportional relationship

Step-by-step explanation:

We can represent this relationship with an equation.

y = 30x + 15

where x would represent the months and y would be the total cost. The 15 would be the initial fee, which only occurs once.

A) Using the relationship \(y = 30x + 15\), we can substitute 2 for x, since that would represent the months.

\(y = 30x + 15\\y = 30(2) + 15\\y = 75\)

It would be 75 dollars.

B) The total cost for x months would just be the relationship

\(y = 30x + 15\)

C) 2 years would represent 24 months. The screen shot below would represent the relationship. The y axis would be the total cost in dollars and the x axis would be the months. (24, 735)

D) Yes, there is a proportional relationship because as the time (months) progress or increases so does the price (dollars). The graph is linear too, which means it increases.

Answer:

\( \rm \displaystyle \frac{d }{dx} \sqrt{x} = \frac{ 1 }{ 2\sqrt{x } } \)

Step-by-step explanation:

we want to differentiate the following by using limit:

\( \displaystyle \frac{d}{dx} \sqrt{x} \)

derivative definition by limit given by

\( \rm \displaystyle \frac{d}{dx} = \lim _{\Delta x \to 0} \left( \frac{f(x + \Delta x) - f(x)}{ \Delta x} \right) \)

given that,

f(x)=√x

so,

f(x+∆x)=√(x+∆x)

thus substitute:

\( \rm \displaystyle \frac{d }{dx} \sqrt{x} = \lim _{\Delta x \to 0} \left( \frac{ \sqrt{x + \Delta x}- \sqrt{x} }{ \Delta x} \right) \)

multiply both the numerator and denominator by the conjugate of the numerator:

\( \rm \displaystyle \frac{d }{dx} \sqrt{x} = \lim _{\Delta x \to 0} \left( \frac{ \sqrt{x + \Delta x}- \sqrt{x} }{ \Delta x} \times \frac{ \sqrt{x + \Delta x} + \sqrt{x} }{\sqrt{x + \Delta x} + \sqrt{x}} \right) \)

simplify which yields:

\( \rm \displaystyle \frac{d }{dx} \sqrt{x} = \lim _{\Delta x \to 0} \left( \frac{ (\sqrt{x + \Delta x}) ^{2} - x }{ \Delta x(\sqrt{x + \Delta x} + \sqrt{x})} \right) \)

simplify square:

\( \rm \displaystyle \frac{d }{dx} \sqrt{x} = \lim _{ \Delta x \to 0} \left( \frac{ x + \Delta x - x }{ \Delta x(\sqrt{x + \Delta x} + \sqrt{x})} \right) \)

collect like terms:

\( \rm \displaystyle \frac{d }{dx} \sqrt{x} = \lim _{\Delta x \to 0} \left( \frac{ \Delta x }{ \Delta x(\sqrt{x + \Delta x} + \sqrt{x})} \right) \)

reduce fraction:

\( \rm \displaystyle \frac{d }{dx} \sqrt{x} = \lim _{\Delta x \to 0} \left( \frac{ 1 }{ (\sqrt{x + \Delta x} + \sqrt{x})} \right) \)

get rid of ∆x as we are approaching its to 0

\( \rm \displaystyle \frac{d }{dx} \sqrt{x} = \frac{ 1 }{ \sqrt{x } + \sqrt{x}} \)

simplify addition:

\( \rm \displaystyle \frac{d }{dx} \sqrt{x} = \frac{ 1 }{ 2\sqrt{x } } \)

and we are done!

The rate increases by a factor of 9 when the concentration is tripled.

It is given to us that the rate law is -

\(R=k(NO_{2} )^{2}\) ----- (1)

We have to find out the change in the rate if the concentration is tripled.

When the concentration is tripled, we can rewrite the equation (1) as -

\(R_{new} =k(3*NO_{2} )^{2}\\= > R_{new} =9*k(NO_{2} )^{2}\\= > R_{new} =9R\)[From equation (1)]

Thus, we see that the rate increases by a factor of 9 when the concentration is tripled.

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Answer:

5.6 ft

Step-by-step explanation:

One if the functions of a protein macromolecule is: c. moving material in and out of cells

Proteins can be described as a complex macromolecules that are responsible for several key functions such as the regulation of cells, tissue, and organs of living organisms including their structure.

Proteins also help in performing the following:

Regulation of gene expression

Structural support, and

Many other cellular processes.

Therefore, a function of a protein macromolecule is: c. moving material in and out of cells.

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The remaining 50.4% of the variance has not been accounted for, and it could be due to other factors that are not captured by the two variables being studied.

If the correlation between two variables is .496, it means that 49.6% of the variance has been accounted for. This is because the correlation coefficient measures the strength and direction of the linear relationship between the two variables, and it ranges from -1 to 1.

A correlation of 1 indicates a perfect positive linear relationship, while a correlation of -1 indicates a perfect negative linear relationship. In this case, a correlation of .496 indicates a moderate positive linear relationship.

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the slopes of the sides do not matter. It's the fact that AD and BC are parallel and AB and DC are NOT parallel that determines it to be a trapezoid.

Answer:

Yes

Step-by-step explanation:

I believe it would be :) sorry if it's wrong I'm just a 8th grader

Answer:

Set of all real numbers

Step-by-step explanation:

When we talk of domain, we mean the possible values of x that the equation can take without being undefined

So x-values that makes the equation defined are the domain of the graph

From the diagram, we can see that the graph extends from negative infinity to positive infinity

What this mean is that the possible values here come from the top right and extends to the left

So this means that the range of possible values are the set of all real numbers

The system of equations has infinite solutions, both equations represent the same line.

Here we have the following system of equations:

-3x+6y=12

2y=x+4

And we want to solve this by substitution, first, we can rewrite the first equation as:

-3x + 3*(2y) = 12

Now we can substitute the second equation 2y = x + 4 in the parenthesis, we will get:

-3x + 3*(x + 4) = 12

Now we can solve this for x.

-3x + 3x + 12 = 12

12 = 12

So this is true for any value of x, which means that both equations represent the same line (thus the system has infinite solutions).

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A damper element always dissipates energy because it converts the kinetic energy of a moving object into heat energy, which is described mathematically by the equations F = -c*v and E = 0.5*c*v^2.

A damper element, also known as a viscous damper or a shock absorber, is a mechanical component that is used to dissipate energy in a system. The damper element does this by converting the kinetic energy of a moving object into heat energy. This process can be described mathematically using the following equation:

F = -c*v

Where F is the force applied by the damper element, c is the damping coefficient, and v is the velocity of the object. This equation shows that the force applied by the damper element is always in the opposite direction of the velocity of the object, meaning that the damper element always works to slow down the object and dissipate its energy.

The amount of energy dissipated by the damper element can also be calculated using the following equation:

E = 0.5*c*v^2

Where E is the energy dissipated by the damper element, c is the damping coefficient, and v is the velocity of the object. This equation shows that the amount of energy dissipated by the damper element is proportional to the square of the velocity of the object, meaning that the damper element is more effective at dissipating energy when the object is moving at higher speeds.

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So, The correct match of these quadratic equations are
Equation A has a solution x = 3 and x = 0.

Equation B has a solution x = 2 and x = 4.

Equation C has a solution x = -3 and x = 0.

Equation D has a solution x = 4 and x = 0.

According to the equation

we have given that the some equation with there values of the x and we have to find and match the correct statement with the given values of x.

So, For this purpose, we know that the

The given quadratic equations are:

A. 24x – 6x^2 = 0 and 2x(3x) = 0 with solution x = 0, x = -3

B. 14x – 7x^2 = 0 and 6x(4 – x) = 0 with solution x = 0, x = 4

C. 2x^2+ 6x = 0 and x(4 – x) = 0 with solution x = 0, x = 4

D. 4x – x^2 = 0 and 7x(2 – x) = 0 with solution x = 0, x = 2

And now we solve it

So,

Take A.

24x – 6x^2 = 0 and 2x(3x) = 0

6x(3 -x) = 0 And 6x^2 = 0

here x = 3 and x = 0.

And

Take B.

14x – 7x^2 = 0 and 6x(4 – x) = 0

7x(2 -x) = 0 And 6x(4 – x)= 0

here x = 2 and x = 4.

And

Take C.

2x^2+ 6x = 0 and x(4 – x) = 0

2x(x +3) = 0 And x(4 – x)= 0

here x = -3 and x = 0.

And

Take D.

4x – x^2 = 0 and 7x(2 – x) = 0

x(4 -x) = 0 And 7x(2 – x)= 0

here x = 4 and x = 0.

So, The correct match of these quadratic equations are
Equation A has a solution x = 3 and x = 0.

Equation B has a solution x = 2 and x = 4.

Equation C has a solution x = -3 and x = 0.

Equation D has a solution x = 4 and x = 0.

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equal to and both stacks have the same number of blocks

Step-by-step explanation:

just trust me!!

Therefore, the predicted difference in sales between two women's clothing stores differing by $30,000 is $217,500, which is option E.

Given a regression equation is y = 5000 + 7.25x, where y is the predicted sales value (in dollars) and x is advertising budget (in dollars).To find the predicted difference in sales of two stores which differ by $30,000 in advertising budget. Here, the slope of the line is 7.25. This means that for every dollar increase in advertising budget, sales will increase by $7.25. Therefore, a $30,000 difference in advertising budget will lead to a difference in sales of:7.25 × 30,000 = 217,500Therefore, the predicted difference in sales between two women's clothing stores differing by $30,000 is $217,500, which is option E.

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The evaluations are:

f(−3) = 9
f(−2) = 4
f(0) = 4
f(2) = 6
f(3) = 7

To evaluate the given piecewise defined function at the indicated values, we need to substitute the given values into the corresponding parts of the function.

Let's evaluate f(−3) first. Since −3 is less than 0, we use the first part of the function f(x)={x^2 if x<0}. Therefore, substituting x = −3 into the function, we get:
f(−3) = (−3)^2 = 9

Next, let's evaluate f(−2). Again, −2 is less than 0, so we use the first part of the function:
f(−2) = (−2)^2 = 4

Moving on to f(0), we see that 0 is not less than 0, so we use the second part of the function f(x)={x+4 if x≥0}. Substituting x = 0 into the function, we get:
f(0) = 0 + 4 = 4

Now, let's evaluate f(2). Since 2 is greater than or equal to 0, we use the second part of the function:
f(2) = 2 + 4 = 6

Finally, let's evaluate f(3). Again, 3 is greater than or equal to 0, so we use the second part of the function:
f(3) = 3 + 4 = 7

So, the evaluations are:
f(−3) = 9
f(−2) = 4
f(0) = 4
f(2) = 6
f(3) = 7

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Answer:

never, never

Step-by-step explanation:

a *( 1/a)

Rewriting

a/a *1

1

This is not equal to -1

ab

Both a and b are negative

(-) * (-) = positive

Never,never

#1

If a is negative

a(1/a)=a/a becomes

Whuch yields 1 not -1

#2

a and b are negative

We know

So their product can't be negative

Answer:

each ribbon should be 3.5(3 and a half or 3 1/2) feet long

Step-by-step explanation:

i divided 14 by 4

Answer:

3 days

Step-by-step explanation:

Let x - be the number of days

Jack: 55 + 4x

Emily: 28 + 13x

To know when they would have the same amount of money, you make the two equations equal to each other.

Hence:

55 + 4x = 28 + 13x

Rearrange:

55 - 28 = 13x - 4x

Simplify

27 = 9x

Divide each side by 9 to make x on its own (this way we would be able to know the number of days when they get the same amount of money)

x = 3 (3 days)

Answer:

3 days

Step-by-step explanation:

jack                          emily

55+4=59             28+13=41

59+4=63              41+13=54

63+4=67               54+13=67

The definite and indefinite integral are both important concepts in calculus. The indefinite integral represents the antiderivative of a function,

which means finding a function whose derivative is the original function. It is often denoted by the symbol "∫" followed by the function to be integrated. The indefinite integral is not unique, as it can have an arbitrary constant of integration.

On the other hand, the definite integral is the signed area between the curve and the x-axis over a specified interval. It is often denoted by the symbol "∫" with limits of integration at the upper and lower bounds of the interval. The definite integral has a definite value, as it is a single number obtained by evaluating the antiderivative at the limits of integration.

In summary, the indefinite integral is a family of functions while the definite integral is a single number. The indefinite integral is used to solve differential equations while the definite integral is used to calculate the area under a curve. Understanding the difference between these two concepts is crucial for success in calculus.

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Answer:

The angle of the unknown measure is 27°.

Step-by-step explanation:

When we look at this angle, we can see it is a 90° angle.  Since we already have 63° of the angle, we just subtract 90° from 63° and we get 27°.  Therefore, 27° is our answer.